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Precision comparison of Integer and Fractional Quantum Hall Effect

28.11.2017

For the Quantum Hall Effect, which is one of the pillars of the "New SI", the material independence of the measured resistance has been under continuous experimental scrutiny. For the first time, this has now been extended to a material where not electrons but composites of magnetic flux quanta and electrons ("composite fermions") carry the current.

The quantum Hall Effect (QHE) can be used to trace electrical resistance to the values of Planck’s constant h and of elementary charge e. Combined with the Josephson Effect, which uses superconducting circuits to trace electrical voltage to h and e, not only electrical units can be based on these constants, but also the kilogram, unit of mass. These effects constitute key foundations of the "New SI", which is fully based on fundamental constants. The theory describing the QHE is, however, rather complex. Therefore, the material independence ("universality") of the QHE has been repeatedly challenged by purely experimental tests in various materials.

For the first time, such a precision test of universality was now performed at PTB in a material where electrical current is no longer carried by electrons, but by composites of electrons bound to magnetic flux quanta. A semiconductor device hosting such "composite fermions" (which carry only 1/3 of an elementary charge) exhibits a quantized Hall resistance in certain ranges of magnetic field, like usual devices where electrons carry the current. However, the quantized resistance values are now no longer integer, but fractional submultiples of the constant h/e2, which explains the names integer and fractional QHE for the effects.

To measure this resistance with high precision, several problems need to be solved. First there is the need for extremely pure semiconductor material, which further must be exposed to very low temperatures only some hundredths of a degree above absolute zero to allow formation of the composite fermions. Moreover, magnetic fields must be applied, which are even higher than in the integer QHE case. Researchers have succeeded in realizing these experimental conditions for many years. Much more challenging is the limitation of the measurement current to less than a percent of the usual current. Too high a current lets the composite fermions quasi "melt-away", whereas small currents incur large measurement uncertainties.

The improvement of PTB’s precision resistance setup was the key to solving this problem: With newly developed current sources and a new null detector, and with many improvements in other parts of the setup, these socalled cryogenic current comparator (CCC) bridges now achieve relative measurement uncertainties in the range of some 10-8 also at currents in the nanoampere range. For the relative difference between integer and fractional quantized Hall resistance a value of (5,3 ± 6,3)·10-8 was found, at a confidence level of 95%.

This comparison of integer and fractional quantized Hall Effect has confirmed the expected universality within this unprecedented small relative uncertainty and thus further underpinned the foundations of the "New SI". The result will soon be published in the journal Metrologia.

Figure: Over certain ranges of magnetic field, fractional (blue curve) und integer Quantum-Hall-Effect (green curve) lead to resistances, which are only determined by the fundamental constants h and e and integer numbers. The theoretically predicted ratio of 1:6 of the resistances marked by arrows was now confirmed in experiments with an uncertainty of some 10-8.